In this paper, M-estimators, where M stands for maximum likelihood, used in robust regression theory for linear parametric regression problems will be generalized to nonparametric maximum likelihood fuzzy neural networks (MFNNs) for nonlinear regression problems. Emphasis is put particularly on the robustness against outliers. This provides alternative learning machines when faced with general ...

A common problem in multiple regression models is multicollinearity, which produces undesirable effects on the least squares estimator. To circumvent this problem, two well known estimation procedures are often suggested in the literature. They are Generalized Ridge Regression (GRR) estimation suggested by Hoerl and Kennard [8] and the Jackknifed Ridge Regression (JRR) estimation suggested by S...

Let X ∼ Np(θ, σIp) and W ∼ σχm, where both θ and σ are unknown, and X is independent of W . Optimal estimation of θ with unknown σ is a fundamental issue in applications but basic theoretical issues remain open. We consider estimation of θ under squared error loss. We develop sufficient conditions for prior density functions such that the corresponding generalized Bayes estimators for θ are adm...

Efficient estimation of the regression coefficients in longitudinal data analysis requires a correct specification of the covariance structure. Existing approaches usually focus on modeling the mean with specification of certain covariance structures, which may lead to inefficient or biased estimators of parameters in the mean if misspecification occurs. In this article, we propose a data-drive...

This paper introduces a new biased estimator, namely, almost unbiased Liu estimator (AULE) of β for the multiple linear regression model with heteroscedastics and/or correlated errors and suffers from the problem of multicollinearity. The properties of the proposed estimator is discussed and the performance over the generalized least squares (GLS) estimator, ordinary ridge regression (ORR) esti...

In many situations, data follow a generalized linear model in which the mean of the responses is modelled, through a link function, linearly on the covariates. In this paper, robust estimators for the regression parameter are considered in order to build test statistics for this parameter when missing data occur in the responses. We derive the asymptotic behaviour of the robust estimators for t...

In this paper, we consider the prediction problem in multiple linear regression model in which the number of predictor variables, p, is extremely large compared to the number of available observations, n. The least squares predictor based on a generalized inverse is not efficient. We propose six empirical Bayes estimators of the regression parameters. Three of them are shown to have uniformly l...

Partial linear model is very flexible when the relation between the covariates and responses, either parametric and nonparametric. However, estimation of the regression coefficients is challenging since one must also estimate the nonparametric component simultaneously. As a remedy, the differencing approach, to eliminate the nonparametric component and estimate the regression coefficients, can ...